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Simplifying (u^{3}+ -8) + -3u + 8 = 0 Reorder the terms: (-8 + u^{3}) + -3u + 8 = 0 Remove parenthesis around (-8 + u^{3}) -8 + u^{3}+ -3u + 8 = 0 Reorder the terms: -8 + 8 + -3u + u^{3}= 0 Combine like terms: -8 + 8 = 0 0 + -3u + u^{3}= 0 -3u + u^{3}= 0 Solving -3u + u^{3}= 0 Solving for variable 'u'. Factor out the Greatest Common Factor (GCF), 'u'. u(-3 + u^{2}) = 0## Subproblem 1

Set the factor 'u' equal to zero and attempt to solve: Simplifying u = 0 Solving u = 0 Move all terms containing u to the left, all other terms to the right. Simplifying u = 0## Subproblem 2

Set the factor '(-3 + u^{2})' equal to zero and attempt to solve: Simplifying -3 + u^{2}= 0 Solving -3 + u^{2}= 0 Move all terms containing u to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + u^{2}= 0 + 3 Combine like terms: -3 + 3 = 0 0 + u^{2}= 0 + 3 u^{2}= 0 + 3 Combine like terms: 0 + 3 = 3 u^{2}= 3 Simplifying u^{2}= 3 Take the square root of each side: u = {-1.732050808, 1.732050808}## Solution

u = {0, -1.732050808, 1.732050808}

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